Logarithms 101

​YAYY Its Logarithms!!

Logarithms are the inverse of exponents. A logarithm (or log) is the mathematical expression used to find the amount of times must a number (base) be raised in order to reach a certain number 

logarithmic form is log_b a = x

exponential form is b^x = a

The two basic properties of logarithms are log of 1 and log of the same number as the base. Log of 1 rule states that log_b 1 = 0 means that the logarithm of 1 is always zero, no matter what the base of the logarithm is. This is because any number raised to 0 equals 1. The log of the same number as the base is always 1.

log_b 1 = 0 log_b b = 1

Logarithms

A natural logarithm is a logarithm that has an e base. We use the ln when we are trying to find the log with a base of e.

Natural logarithm

A logarithm with a base of 10 is called a common logarithm and doesn't have to be written with the base.

​Common logarithm

​log ₁₀ x

​log _e x

Draw

Draw the logarithmic form of 2^-1 = $$\frac{1}{2}$$

Product property is when the product is the logarithm could be separated into addition using the factors of the previous logarithms. This property says that the logarithm of a product is the sum of the logarithms of its factors.

​ Product Property

Multiple Choice

Using the Product Property, Expand Log₃ (20)

•  log₃ (4) + log₃ (5)

•  log3 (4) + log3 (5)

• log₃ (4) - log₃ (5)

• log3 (4) - log3 (5)

Quotient property is when… this property says that the logarithm of a quotient is equal to the difference of the logarithms numerator and denominator.

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Quotient Property

​Log₆ 80/16

​Log₆ (80) - Log₆ (16)

Multiple Choice

Expand this logarithm.

• A

• C

• D

• B

​Power property is when the logarithm expression changes around without changing the numbers. This property says that the logarithm of a power is equal to the product of the logarithm and the exponent.

Power Property

​log_a m^x = X log_{a m}

​log₅ 5² = 2 log₅ 5

​log₈ x⁶ = 6 log₈ x

Multiple Choice

Expand: Log₇ 3^2x

• Log₇ (3)^x + Log₇ (1)^x

• 2x Log₇ (3)

• 3 Log₇ (2x)

• Log₇ 3 = 0

Multiple Choice

What is the logarithmic form of $$3^{-4}=\frac{1}{81}$$

• Log₃ (1/81) =-4

• Log_-4 3 = 1/81

• Log₃ (1) - Log₃ (81)

• Log₃ (81)^-4

Multiple Choice

True or False?

• True

• False

• Nylah White-Logan

Even though it doesn’t seem like it, Logarithms are being used to solve issues in everyday life with stuff, like measuring the magnitude of earthquakes, the exponential growth and decay of money, the pH of chemicals, and the measurement of noise. When doing this project, I used logarithms to find the exponential growth of my credit card and it helped. Many students can use this quizzes interactive lesson in order to better understand the basics of logarithms before getting deeper into the complexity of logarithms. When doing this project I had to relearn logarithms and was able to better comprehend why they were the inverse of exponents and how ln and e are the same thing.

​Synopsis

Poll

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